As discussed in the previous chapter (see e.g., [1]}[2]}), the relationship between Hermitian operators \(\hat{A}\)  that act on a complex Hilbert space and e-functionals \(\tilde{A}\)  defined over the e-phase space \(\Gamma \)  is given by
\(\tilde{A}[\rho ,\Phi ] = \int D\chi \Psi ^{*}\hat{A}\Psi = \left\langle \hat{A} \right\rangle ~.\) 
